Consider the following game. There are two players, 1 and 2. They will play either Matching Quarters version A (with player 1 moving first), Modified Matching Quarters version A (where player 2 moves first), or Matching Quarters version B (where both players move simultaneously). Nature selects randomly among these alternatives; each game is chosen with equal likelihood. Nature’s choose is observed by both players. For the purposes of payoff in this question, player 1 wins (+2) with a match (player 2 losing (-2)), player 2 wins when there is not a match (-2, +2).
a. Draw the extensive form of this game.
b. Determine the strategy sets for each player in this game.
c. Draw the normal form for this game.